Pragmatically, in data analysis tasks, what you do is a separate preliminary data collection that you only use to decide the priors (the whole data analysis structure, really) and then collect data again on which you run the actual analysis. This applies to non-Bayesian data analysis as well. This duplicated data collection helps you stay objective and not sneak into the prior any information which would not be Bayes-kosher to glean from the data. Of course it’s less efficient because you are not using all the data in the final analysis.
Pragmatically, in data analysis tasks, what you do is a separate preliminary data collection that you only use to decide the priors (the whole data analysis structure, really) and then collect data again on which you run the actual analysis. This applies to non-Bayesian data analysis as well. This duplicated data collection helps you stay objective and not sneak into the prior any information which would not be Bayes-kosher to glean from the data. Of course it’s less efficient because you are not using all the data in the final analysis.